Theory of the Cathode Sheath in a Low-Density Gas Discharge

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Abstract
The space-charge equations of a low-density gas discharge are derived and applied in the present report to the study of potential distributions in the cathode sheath. In order to facilitate mathematical computation, the contribution of secondary electrons and charge exchange to the potential distribution is neglected. The space charge is generated, consequently, by the primary electrons of the hot cathode and the ions resulting from volume ionization of the gas in the sheath. The effect of arbitrary positive-ion currents issuing from the positive column to the sheath is also examined.

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